8.7.14 problem 14

Internal problem ID [820]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 14
Date solved : Monday, January 27, 2025 at 03:09:18 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=10\\ y^{\prime }\left (2\right )&=15 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=0,y(2) = 10, D(y)(2) = 15],y(x), singsol=all)
 

\[ y = 3 x^{2}-\frac {16}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

DSolve[{x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==0,{y[2]==10,Derivative[1][y][2]==15}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x^5-16}{x^3} \]