Internal problem ID [14741]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -1, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {4 x^{\frac {7}{2}}}{5}-\frac {9 x}{5} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 19
DSolve[{2*x^2*y''[x]-7*x*y'[x]+7*y[x]==0,{y[1]==-1,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} x \left (4 x^{5/2}-9\right ) \]