Internal problem ID [10205]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
27. Clairaut equation. Page 56
Problem number: Ex 4.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {{\mathrm e}^{2 y} \left (y^{\prime }\right )^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.36 (sec). Leaf size: 31
dsolve(exp(2*y(x))*diff(y(x),x)^3+(exp(2*x)+exp(3*x))*diff(y(x),x)-exp(3*x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (-\left (c_{1}+1\right ) \left ({\mathrm e}^{-2 x} c_{1}^{2}-2 c_{1} {\mathrm e}^{-x}+1\right )\right )}{2}+x \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[Exp[2*y[x]]*(y'[x])^3+(Exp[2*x]+Exp[3*x])*y'[x]-Exp[3*x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out