Internal problem ID [7633]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _Chini]
Solve \begin {gather*} \boxed {y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.089 (sec). Leaf size: 64
dsolve(diff(y(x),x) - a*y(x)^n - b*x^(n/(1-n))=0,y(x), singsol=all)
\[ -\left (\int _{\textit {\_b}}^{y \relax (x )}\frac {x^{\frac {n}{n -1}}}{\left (a x \left (n -1\right ) \textit {\_a}^{n}+\textit {\_a} \right ) x^{\frac {n}{n -1}}+b x \left (n -1\right )}d \textit {\_a} \right )+\frac {\ln \relax (x )}{n -1}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 117
DSolve[y'[x] - a*y[x]^n - b*x^(n/(1-n))==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\int _1^{\left (\frac {a x^{-\frac {n}{1-n}}}{b}\right )^{\frac {1}{n}} y(x)}\frac {1}{K[1]^n-\left (\frac {(-1)^n b^{1-n} (n-1)^{-n}}{a}\right )^{\frac {1}{n}} K[1]+1}dK[1]=\int _1^xb K[2]^{\frac {n}{1-n}} \left (\frac {a K[2]^{-\frac {n}{1-n}}}{b}\right )^{\frac {1}{n}}dK[2]+c_1,y(x)\right ] \]