Internal problem ID [7385]
Book: First order enumerated odes
Section: section 1
Problem number: 69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-{\mathrm e}^{x +y} x=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x)=x*exp(x+y(x))+sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\cos \left (x \right )-\ln \left (-c_{1} -\left (\int x \,{\mathrm e}^{x -\cos \left (x \right )}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 3.93 (sec). Leaf size: 100
DSolve[y'[x]==x*Exp[x+y[x]]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^x\left (-e^{K[1]-\cos (K[1])} K[1]-e^{-\cos (K[1])-y(x)} \sin (K[1])\right )dK[1]+\int _1^{y(x)}-e^{-\cos (x)-K[2]} \left (e^{\cos (x)+K[2]} \int _1^xe^{-\cos (K[1])-K[2]} \sin (K[1])dK[1]-1\right )dK[2]=c_1,y(x)\right ] \]