Solve the differential equation ${{x}^{4}}\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=x+3$, gi

Question

Solve the differential equation ${{x}^{4}}\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=x+3$, given that the point $\left( 1,\frac{23}{6} \right)$ is a stationary point of the solution curve.[4]

Accepted Answer

When $x=1$, $y=\frac{23}{6}\Rightarrow D=\frac{4}{3}$. Hence, $y=\frac{1}{2x}+\frac{1}{2{{x}^{2}}}+\frac{3x}{2}+\frac{4}{3}$.

2023 MI P1 Q2

2023 MI P1 Q2

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