Internal problem ID [8255]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 675.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+x^{3} a -x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(y(x),x) = (y(x)+x^3*a*exp(x)+a*x^4+x^3*a-x*y(x)^2*exp(x)-x^2*y(x)^2-x*y(x)^2)/x,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (\frac {x^{3} \sqrt {a}}{3}+x \,{\mathrm e}^{x} \sqrt {a}+\frac {\sqrt {a}\, x^{2}}{2}-{\mathrm e}^{x} \sqrt {a}+c_{1} \sqrt {a}\right ) x \sqrt {a} \]
✓ Solution by Mathematica
Time used: 5.985 (sec). Leaf size: 44
DSolve[y'[x] == (a*x^3 + a*E^x*x^3 + a*x^4 + y[x] - x*y[x]^2 - E^x*x*y[x]^2 - x^2*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {a} x \tanh \left (\frac {1}{6} \sqrt {a} \left ((2 x+3) x^2+6 e^x (x-1)+6 c_1\right )\right ) \\ \end{align*}