12.2.31 problem 31

Internal problem ID [1567]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 31
Date solved : Monday, January 27, 2025 at 05:00:26 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+2 y&=8 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve([x*diff(y(x),x)+2*y(x)=8*x^2,y(1) = 3],y(x), singsol=all)
 

\[ y = \frac {2 x^{4}+1}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 14

DSolve[{x*D[y[x],x]+2*y[x]==8*x^2,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x^2+\frac {1}{x^2} \]