Internal problem ID [14776]
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: 66 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = a, y^{\prime }\left (1\right ) = b] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 25
dsolve([6*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)-y(x)=0,y(1) = a, D(y)(1) = b],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\frac {2 \left (a +3 b \right ) x^{\frac {5}{6}}}{5}+\frac {3 a}{5}-\frac {6 b}{5}}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 36
DSolve[{6*x^2*y''[x]+5*x*y'[x]-y[x]==0,{y[1]==a,y'[1]==b}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {a \left (2 x^{5/6}+3\right )+6 b \left (x^{5/6}-1\right )}{5 \sqrt [3]{x}} \]