Internal problem ID [3391]
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]
\[ \boxed {y^{\prime }-a f \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x) = a*f(y(x)),y(x), singsol=all)
\[ x -\left (\int _{}^{y \left (x \right )}\frac {1}{a f \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.295 (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*}