Internal problem ID [2012]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{3} y^{\prime }+y^{4} x=x \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 114
dsolve(y(x)^3*diff(y(x),x)+x*y(x)^4=x*exp(-x^2),y(x), singsol=all)
\begin{align*} y = {\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} y = -{\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} y = -i {\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} y = i {\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]^4*y'[x]+x*y[x]^4==x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
Not solved