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多选题设是方程的两个解,则(为任意常数)

A. 一定是该方程的解

B. 可能是该方程的解

C. 一定是该方程的通解

D. 可能是该方程的通解

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学科：默认课程

时间：2026-04-03 01:58:44

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下列微分方程中,可以分离变量的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/312fc69bb1dcc599c921ac30aa9ec990.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/8bffec186129d1d65485ff31ceda0787.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/ff388086797858d55082577cae9b933b.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/fed8f53b482d260e2cbbeb6d036049b7.png">

微分方程<img src="https://tihai-oss-cloud.itihey.com/img/21d18f511fd09ad440fcc0c5be79b16b.png">的通解为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/ba60cd6f4b9f87f4790d83a2995395a3.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/dfa01ca689b2027617bb296fb6501e61.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/b7c25cd4bf77026da97cac76e3794ad5.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/90ed3b615885631851194a43d24db62e.png">

微分方程<img src="https://tihai-oss-cloud.itihey.com/img/5e75b3a0cec5a88ce025e6a4f2b988a7.png"> 的通解是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/cbb079abdb735e28a7c74a6ce907905d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/4ac50d67a0637c50e4c52bf39bdd7b37.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/aae8cf6a38f5408b3a010118d53fe76c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/754af9a2e910ded82f3c9c25acef81ee.png">

齐次微分方程<img src="https://tihai-oss-cloud.itihey.com/img/2490afaf78bfc2cf30b7b58f86deeab9.png">的通解是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/a3ffa1b99337bc36f9c47d018df74de2.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/f81a9cc4894b2502d8a57fcce03a70e3.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/4510b1b8a9cadff28d4140995b466c24.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/3b3f4433504d3db319a18f800b36d85f.png">

微分方程<img src="https://tihai-oss-cloud.itihey.com/img/e0ab5700713add64adf7e82aae76ac10.png">的通解为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/9a1e56bd874fe57f4a6a66c34dbc021a.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/4c8acc059f6d91e15ce7a7f57a720b7b.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3184c664156f39a58108ead89b6d2291.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/ae88c4dbc276f0efe3d5e5860ea6726d.png">

以<img src="https://tihai-oss-cloud.itihey.com/img/be90509704f65d4c094b69f3b3d22e90.png">为通解的微分方程是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/9c3b2ff912db5eee36883ef8833a4760.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/a95f987baae75d77e0a0e40590c494d8.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/89c2fee7b493439a4b10c561c0844dbd.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/6a21a7bb9ebb4fe352a607d4fbbbb898.png">

若方程<img src="https://tihai-oss-cloud.itihey.com/img/665f48f4e7c98d150a67579d7b99bfc8.png">的通解为<img src="https://tihai-oss-cloud.itihey.com/img/7636e50ffa375d100a3a1518ea8ee714.png">,那么<img src="https://tihai-oss-cloud.itihey.com/img/129cf373be336acb130f5a1f71cc20d6.png">的值为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/d2a69f3ddd6495d49d7298ea5fc80de9.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/6bc6d01a715e14bfa1968182be596a62.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/adc72b4d4092599041fe3fa239209f9c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/291130c14d9629de1e010043ee66df60.png">

下列哪项是微分方程<img src="https://tihai-oss-cloud.itihey.com/img/ceca7ef415e2cc00049d6b70bff3437f.png">的一个特解()

A. <img src="https://tihai-oss-cloud.itihey.com/img/75067d6de3f3502fa6d2ee9ce5e8db23.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/e07523225aebae51be8b9204330332f3.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/4978aba6c9e84c55f6cc63b40ed85251.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/5ba72f20eecc711cac525127c54e27b1.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/65789a99603a1c5b60659c85d294fd24.png">是方程<img src="https://tihai-oss-cloud.itihey.com/img/6b565626fb85be74a3cf4b5101a8b2a5.png">的两个解,则<img src="https://tihai-oss-cloud.itihey.com/img/dbb2823a5a09c2805842eb56752b5ebe.png">(<img src="https://tihai-oss-cloud.itihey.com/img/7b98c1dd776ccd2ad72451bcf43a4ae7.png">为任意常数)

A. 一定是该方程的解B. 可能是该方程的解C. 一定是该方程的通解D. 可能是该方程的通解

下列函数组在其定义区间内是线性无关的有( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/c8dce0645d6ee2017adca5a57337817d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/f2a91ef0ee6240a2eb54b00489916f3c.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/e3cf5592d483f6d20e1a7ec6502a4c4c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/9a53870b2c68f312896f3cc1e89be8f4.png">

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