28.2.70 problem 70

Internal problem ID [4513]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 70
Date solved : Monday, January 27, 2025 at 09:22:33 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 41

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

\[ y \left (x \right ) = \frac {7 c_{2} \cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right )+7 c_3 \sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right )+\left (x +7 c_{1} \right ) x^{{3}/{2}}}{7 \sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 57

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

\[ y(x)\to \frac {1}{7} x (x+7 c_1)+\frac {c_2 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )}{\sqrt {x}}+\frac {c_3 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )}{\sqrt {x}} \]