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First order differential equations
Skilled2021-03-08Added 91 answers
xu′(x)=u2−4xu′(x)1u2−4=11u2−4du=1xdxIntegrating on both sides∫1u2−4du=∫1xdxThe partial fraction of the left side 1(u+2)(u−2)=−14(x+2)+14(x−2)−14∫1u+2du+14∫1u−2du=∫1xdx−14ln(u+2)du+14ln(u−2)=ln(x)+C1−ln(u+2)du+ln(u−2)=4ln(x)+4C1ln(u−2u+2)=ln(x4)+C2(u−2u+2)=(x4)+eC2=x4+Cu=−2(C+x4)−C+x4
Expert2021-12-25Added 2575 answers
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