Internal problem ID [2967]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 219.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime } x +n y-f \relax (x ) g \left (x^{n} y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.058 (sec). Leaf size: 33
dsolve(x*diff(y(x),x)+n*y(x) = f(x)*g(x^n*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int x^{n -1} f \relax (x )d x \right )+\int _{}^{\textit {\_Z}}\frac {1}{g \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right ) x^{-n} \]
✓ Solution by Mathematica
Time used: 1.986 (sec). Leaf size: 41
DSolve[x y'[x]+ n y[x]==f[x] g[x^n y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{x^n y(x)}\frac {1}{g(K[1])}dK[1]=\int _1^xf(K[2]) K[2]^{n-1}dK[2]+c_1,y(x)\right ] \]