83.47.3 problem Ex 3 page 80

Internal problem ID [19580]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 3 page 80
Date solved : Tuesday, January 28, 2025 at 01:59:53 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 27

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

\[ y \left (x \right ) = x \left (-\frac {3 \ln \left (x \right )^{2}}{2}+\left (x +c_3 -3\right ) \ln \left (x \right )+\left (c_{2} -2\right ) x +c_{1} -3\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 36

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

\[ y(x)\to -\frac {3}{2} x \log ^2(x)+x ((-2+c_3) x-3+c_1)+x (x-3+c_2) \log (x) \]