57.1.69 problem 69

Internal problem ID [9053]
Book : First order enumerated odes
Section : section 1
Problem number : 69
Date solved : Monday, January 27, 2025 at 05:31:36 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 29

dsolve(diff(y(x),x)=x*exp(x+y(x))+sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.158 (sec). Leaf size: 100

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

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