Internal problem ID [6633]
Book: First order enumerated odes
Section: section 1
Problem number: 70.
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 }-5 \,{\mathrm e}^{x^{2}+20 y}-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 30
dsolve(diff(y(x),x)=5*exp(x^2+20*y(x))+sin(x),y(x), singsol=all)
\[ y \relax (x ) = -\cos \relax (x )-\frac {\ln \left (-20 c_{1}-100 \left (\int {\mathrm e}^{x^{2}} {\mathrm e}^{-20 \cos \relax (x )}d x \right )\right )}{20} \]
✓ Solution by Mathematica
Time used: 6.863 (sec). Leaf size: 140
DSolve[y'[x]==5*Exp[x^2+20*y[x]]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^x-\frac {1}{100} e^{-20 \cos (K[1])-20 y(x)} \left (\sin (K[1])+5 e^{K[1]^2+20 y(x)}\right )dK[1]+\int _1^{y(x)}-\frac {1}{100} e^{-20 \cos (x)-20 K[2]} \left (100 e^{20 \cos (x)+20 K[2]} \int _1^x\left (\frac {1}{5} e^{-20 \cos (K[1])-20 K[2]} \left (\sin (K[1])+5 e^{K[1]^2+20 K[2]}\right )-e^{K[1]^2-20 \cos (K[1])}\right )dK[1]-1\right )dK[2]=c_1,y(x)\right ] \]