73.15.78 problem 22.15 (e)

Internal problem ID [15509]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (e)
Date solved : Tuesday, January 28, 2025 at 08:00:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y&=4 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

dsolve(3*x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+3*y(x)=4*x^3,y(x), singsol=all)
 

\[ y = x^{{1}/{3}} c_{1} +x^{3} \left (c_{2} +\frac {\ln \left (x \right )}{2}-\frac {3}{16}\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 33

DSolve[3*x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+3*y[x]==4*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^3 \log (x)+\left (-\frac {3}{16}+c_2\right ) x^3+c_1 \sqrt [3]{x} \]