74.15.41 problem 41

Internal problem ID [16480]
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
Date solved : Tuesday, January 28, 2025 at 09:09:04 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+y&=x^{3} \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: 0.023 (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)
 

\[ y = \frac {8 \left (3-5 \ln \left (x \right )\right ) \sqrt {x}}{25}+\frac {x^{3}}{25} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 25

DSolve[{4*x^2*D[y[x],{x,2}]+y[x]==x^3,{y[1]==1,Derivative[1][y][1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{25} \sqrt {x} \left (x^{5/2}-40 \log (x)+24\right ) \]