AP EAMCET · Maths · Differential Equations
\(y+x^2=\frac{d y}{d x}\) has the solution
- A \(y+x^2+2 x+2=c e^x\)
- B \(y+x+2 x^2+2=c e^x\)
- C \(y^2+x+x^2+2=c e^{2 x}\)
- D \(y+x+x^2+2=c e^{2 x}\)
Answer & Solution
Correct Answer
(A) \(y+x^2+2 x+2=c e^x\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} y+x^2 & =\frac{d y}{d x} \\ \Rightarrow \quad \frac{d y}{d x}-y & =x^2 \end{aligned} \] It is a linear differential equation. On comparing with \(\frac{d y}{d x}+P y=Q\), we get…
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