Internal problem ID [9584]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, First-Order differential equations
Problem number: 1.1.3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-f \relax (x ) g \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(x),x)=f(x)*g(y(x)),y(x), singsol=all)
\[ \int f \relax (x )d x -\left (\int _{}^{y \relax (x )}\frac {1}{g \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.29 (sec). Leaf size: 42
DSolve[y'[x]==f[x]*g[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{g(K[1])}dK[1]\&\right ]\left [\int _1^xf(K[2])dK[2]+c_1\right ] \\ y(x)\to g^{(-1)}(0) \\ \end{align*}