Internal problem ID [1947]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {3 y x^{2}+y^{2} x +\left (x^{3}+y x^{2}+\sin \left (y\right )\right ) y^{\prime }=-{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve((3*x^2*y(x)+x*y(x)^2+exp(x))+(x^3+x^2*y(x)+sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {x^{2} y^{2}}{2}+x^{3} y+{\mathrm e}^{x}-\cos \left (y\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.377 (sec). Leaf size: 32
DSolve[(3*x^2*y[x]+x*y[x]^2+Exp[x])+(x^3+x^2*y[x]+Sin[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^3 y(x)+\frac {1}{2} x^2 y(x)^2-\cos (y(x))+e^x=c_1,y(x)\right ] \]