57.1.70 problem 70

Internal problem ID [9054]
Book : First order enumerated odes
Section : section 1
Problem number : 70
Date solved : Monday, January 27, 2025 at 05:31:38 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 33

dsolve(diff(y(x),x)=5*exp(x^2+20*y(x))+sin(x),y(x), singsol=all)
 

\[ y = -\cos \left (x \right )-\frac {\ln \left (20\right )}{20}-\frac {\ln \left (-c_{1} -5 \left (\int {\mathrm e}^{x^{2}-20 \cos \left (x \right )}d x \right )\right )}{20} \]

✓ Solution by Mathematica

Time used: 7.700 (sec). Leaf size: 140

DSolve[D[y[x],x]==5*Exp[x^2+20*y[x]]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x-\frac {1}{100} e^{-20 \cos (K[1])-20 y(x)} \left (\sin (K[1])+5 e^{K[1]^2+20 y(x)}\right )dK[1]+\int _1^{y(x)}-\frac {1}{100} e^{-20 \cos (x)-20 K[2]} \left (100 e^{20 \cos (x)+20 K[2]} \int _1^x\left (\frac {1}{5} e^{-20 \cos (K[1])-20 K[2]} \left (\sin (K[1])+5 e^{K[1]^2+20 K[2]}\right )-e^{K[1]^2-20 \cos (K[1])}\right )dK[1]-1\right )dK[2]=c_1,y(x)\right ] \]