76.15.33 problem 34

Internal problem ID [17674]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 34
Date solved : Tuesday, January 28, 2025 at 10:53:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=3 x^{2}+2 \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 31

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

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