29.2.15 problem 40

Internal problem ID [4648]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 40
Date solved : Monday, January 27, 2025 at 09:29:21 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 45

dsolve(diff(y(x),x)+f(x)^2 = diff(f(x),x)+y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-f \left (x \right ) \left (\int {\mathrm e}^{2 \left (\int f \left (x \right )d x \right )}d x \right )+f \left (x \right ) c_{1} +{\mathrm e}^{2 \left (\int f \left (x \right )d x \right )}}{c_{1} -\int {\mathrm e}^{2 \left (\int f \left (x \right )d x \right )}d x} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]+f[x]^2==D[ f[x],x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

Not solved