74.15.32 problem 32

Internal problem ID [16471]
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 : 32
Date solved : Tuesday, January 28, 2025 at 09:08:48 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 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: 0.017 (sec). Leaf size: 13

dsolve([2*x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+7*y(x)=0,y(1) = -1, D(y)(1) = 1],y(x), singsol=all)
 

\[ y = \frac {4 x^{{7}/{2}}}{5}-\frac {9 x}{5} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[{2*x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+7*y[x]==0,{y[1]==-1,Derivative[1][y][1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} x \left (4 x^{5/2}-9\right ) \]