Internal problem ID [2795]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+f \relax (x )^{2}-f^{\prime }\relax (x )-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x)+f(x)^2 = diff(f(x),x)+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = f \relax (x )+\frac {{\mathrm e}^{\int 2 f \relax (x )d x}}{c_{1}-\left (\int {\mathrm e}^{\int 2 f \relax (x )d x}d x \right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]+f[x]^2==f'[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
Not solved