76.13.53 problem 62

Internal problem ID [17635]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 62
Date solved : Tuesday, January 28, 2025 at 10:46:17 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 16

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

\[ y = \frac {4 x^{{5}/{2}}+1}{5 x} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 21

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

\[ y(x)\to \frac {4 x^{5/2}+1}{5 x} \]