Internal problem ID [8157]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 577.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-F \left (\frac {y}{x +a}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 28
dsolve(diff(y(x),x) = F(y(x)/(x+a)),y(x), singsol=all)
\[ y \relax (x ) = -\RootOf \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (-\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +\ln \left (x +a \right )+c_{1}\right ) \left (x +a \right ) \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 243
DSolve[y'[x] == F[y[x]/(a + x)],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{-a F\left (\frac {K[2]}{a+x}\right )-x F\left (\frac {K[2]}{a+x}\right )+K[2]}-\int _1^x\left (\frac {F'\left (\frac {K[2]}{a+K[1]}\right )}{(a+K[1]) \left (a F\left (\frac {K[2]}{a+K[1]}\right )+K[1] F\left (\frac {K[2]}{a+K[1]}\right )-K[2]\right )}-\frac {F\left (\frac {K[2]}{a+K[1]}\right ) \left (\frac {a F'\left (\frac {K[2]}{a+K[1]}\right )}{a+K[1]}+\frac {K[1] F'\left (\frac {K[2]}{a+K[1]}\right )}{a+K[1]}-1\right )}{\left (a F\left (\frac {K[2]}{a+K[1]}\right )+K[1] F\left (\frac {K[2]}{a+K[1]}\right )-K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {F\left (\frac {y(x)}{a+K[1]}\right )}{a F\left (\frac {y(x)}{a+K[1]}\right )+K[1] F\left (\frac {y(x)}{a+K[1]}\right )-y(x)}dK[1]=c_1,y(x)\right ] \]