83.15.3 problem 3

Internal problem ID [19188]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (G) at page 45
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:11:52 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=x^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-6*diff(y(x),x)=1+x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}-\frac {1}{2} x^{2}+\frac {25}{6} x -18 c_3 \right ) {\mathrm e}^{2 x}-6 c_{2} {\mathrm e}^{5 x}+9 c_{1} \right )}{18} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 48

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-6*D[y[x],x]==1+x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{108} \left (-6 x^3+3 x^2-25 x+18 \left (-3 c_1 e^{-2 x}+2 c_2 e^{3 x}+6 c_3\right )\right ) \]