5.19 problem 134

Internal problem ID [2883]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 5
Problem number: 134.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }-a f \relax (y)=0} \end {gather*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x) = a*f(y(x)),y(x), singsol=all)
 

\[ x -\left (\int _{}^{y \relax (x )}\frac {1}{a f \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]

Solution by Mathematica

Time used: 0.265 (sec). Leaf size: 35

DSolve[y'[x]==a f[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[1])}dK[1]\&\right ][a x+c_1] \\ y(x)\to f^{(-1)}(0) \\ \end{align*}