75.6.20 problem 153

Internal problem ID [16776]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 153
Date solved : Tuesday, January 28, 2025 at 09:22:12 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (-\infty \right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.360 (sec). Leaf size: 11

dsolve([x^2*diff(y(x),x)+y(x)=(x^2+1)*exp(x),y(-infinity) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x}+{\mathrm e}^{\frac {1}{x}} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 14

DSolve[{x^2*D[y[x],x]+y[x]==(x^2+1)*Exp[x],{y[-Infinity]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {1}{x}}+e^x \]