Internal problem ID [14740]
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: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([3*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+2*y(x)=0,y(1) = 2, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {9 x^{\frac {1}{3}}}{5}+\frac {x^{2}}{5} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 20
DSolve[{3*x^2*y''[x]-4*x*y'[x]+2*y[x]==0,{y[1]==2,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} \left (x^2+9 \sqrt [3]{x}\right ) \]