74.15.39 problem 39

Internal problem ID [16478]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 39
Date solved : Tuesday, January 28, 2025 at 09:08:58 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=\frac {1}{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 19

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

\[ y = \frac {22 x^{{5}/{2}}-25 x +3}{15 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 24

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

\[ y(x)\to \frac {22 x^{5/2}-25 x+3}{15 x^2} \]