2.15 problem 40

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