Internal problem ID [14750]
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: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }+y=x^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve([4*x^2*diff(y(x),x$2)+y(x)=x^3,y(1) = 1, D(y)(1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {8 \left (3-5 \ln \left (x \right )\right ) \sqrt {x}}{25}+\frac {x^{3}}{25} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 25
DSolve[{4*x^2*y''[x]+y[x]==x^3,{y[1]==1,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{25} \sqrt {x} \left (x^{5/2}-40 \log (x)+24\right ) \]