83.26.13 problem 13

Internal problem ID [19337]
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 : 13
Date solved : Tuesday, January 28, 2025 at 01:34:32 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y&=x^{2}+3 x -4 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(x^3*diff(y(x),x$3)+6*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)+2*y(x)=x^2+3*x-4,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sin \left (\ln \left (x \right )\right ) c_3 +\cos \left (\ln \left (x \right )\right ) c_{2} +\frac {x^{3}}{30}+\frac {3 x^{2}}{10}+c_{1} -2 x}{x} \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 42

DSolve[x^3*D[y[x],{x,3}]+6*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]+2*y[x]==x^2+3*x-4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3+9 x^2-60 x+30 c_2 \cos (\log (x))+30 c_1 \sin (\log (x))+30 c_3}{30 x} \]