Internal problem ID [9010]
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]
\[ \boxed {y^{\prime }-\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \tanh \left (\frac {x^{3} \sqrt {a}}{3}+x \,{\mathrm e}^{x} \sqrt {a}+\frac {x^{2} \sqrt {a}}{2}-{\mathrm e}^{x} \sqrt {a}+c_{1} \sqrt {a}\right ) x \sqrt {a} \]
✓ Solution by Mathematica
Time used: 12.255 (sec). Leaf size: 45
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]
\[ y(x)\to \sqrt {a} x \tanh \left (\frac {1}{6} \sqrt {a} \left (2 x^3+3 x^2+6 e^x (x-1)+6 c_1\right )\right ) \]