Internal problem ID [6631]
Book: First order enumerated odes
Section: section 1
Problem number: 68.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-10 \,{\mathrm e}^{x +y}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 30
dsolve(diff(y(x),x)=10*exp(x+y(x))+x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{3}-\ln \left (-c_{1}-10 \left (\int {\mathrm e}^{x} {\mathrm e}^{\frac {x^{3}}{3}}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.429 (sec). Leaf size: 115
DSolve[y'[x]==10*Exp[x+y[x]]+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}-\frac {1}{10} e^{-K[2]} \left (10 e^{K[2]} \int _1^x-\frac {1}{10} e^{\frac {K[1]^3}{3}-K[2]} K[1]^2dK[1]+e^{\frac {x^3}{3}}\right )dK[2]+\int _1^x\left (\frac {1}{10} e^{\frac {K[1]^3}{3}-y(x)} K[1]^2+e^{\frac {K[1]^3}{3}+K[1]}\right )dK[1]=c_1,y(x)\right ] \]