7.11.57 problem 59

Internal problem ID [378]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 59
Date solved : Monday, January 27, 2025 at 02:47:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

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

\[ y = \frac {x^{2} \left (4 \ln \left (x \right ) c_1 +x^{2}+4 c_2 \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{4} x^2 \left (x^2+8 c_2 \log (x)+4 c_1\right ) \]