51.1.70 problem 70

Internal problem ID [10340]
Book : First order enumerated odes
Section : section 1
Problem number : 70
Date solved : Tuesday, September 30, 2025 at 07:22:21 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*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 33

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

\[ y = -\cos \left (x \right )-\frac {\ln \left (20\right )}{20}-\frac {\ln \left (-c_1 -5 \int {\mathrm e}^{x^{2}-20 \cos \left (x \right )}d x \right )}{20} \]

✓ Mathematica. Time used: 0.254 (sec). Leaf size: 188

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

\[ \text {Solve}\left [\int _1^x-\frac {1}{100} \exp \left (-20 y(x)-\int _1^{K[2]}-20 \sin (K[1])dK[1]\right ) \left (\sin (K[2])+5 e^{K[2]^2+20 y(x)}\right )dK[2]+\int _1^{y(x)}-\frac {1}{100} \exp \left (-20 K[3]-\int _1^x-20 \sin (K[1])dK[1]\right ) \left (100 \exp \left (20 K[3]+\int _1^x-20 \sin (K[1])dK[1]\right ) \int _1^x\left (\frac {1}{5} \exp \left (-20 K[3]-\int _1^{K[2]}-20 \sin (K[1])dK[1]\right ) \left (\sin (K[2])+5 e^{K[2]^2+20 K[3]}\right )-\exp \left (K[2]^2-\int _1^{K[2]}-20 \sin (K[1])dK[1]\right )\right )dK[2]-1\right )dK[3]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*exp(x**2 + 20*y(x)) - sin(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out