83.26.11 problem 11

Internal problem ID [19335]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 01:34:30 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

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

\[ y \left (x \right ) = \frac {x^{2}}{10}-\cos \left (\ln \left (x \right )\right ) c_{2} +\sin \left (\ln \left (x \right )\right ) c_{1} +c_3 \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 28

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

\[ y(x)\to \frac {x^2}{10}-c_1 \cos (\log (x))+c_2 \sin (\log (x))+c_3 \]