44.6.46 problem 46

Internal problem ID [7190]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 46
Date solved : Tuesday, February 04, 2025 at 12:46:06 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } x^{2}-y&=x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 49

dsolve([x^2*diff(y(x),x)-y(x)=x^3,y(1) = 0],y(x), singsol=all)
 

\[ y = \frac {x^{2}}{2}+\frac {x}{2}-\frac {{\mathrm e}^{-\frac {1}{x}} \operatorname {Ei}_{1}\left (-1\right )}{2}-{\mathrm e}^{1-\frac {1}{x}}+\frac {\operatorname {Ei}_{1}\left (-\frac {1}{x}\right ) {\mathrm e}^{-\frac {1}{x}}}{2} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 38

DSolve[{x^2*D[y[x],x]-y[x]==x^3,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-1/x} \left (-\operatorname {ExpIntegralEi}\left (\frac {1}{x}\right )+\operatorname {ExpIntegralEi}(1)+e^{\frac {1}{x}} x (x+1)-2 e\right ) \]