83.5.9 problem 9

Internal problem ID [19104]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 12:56:16 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+3 x^{2} y&=x^{5} {\mathrm e}^{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x)+3*x^2*y(x)=x^5*exp(x^3),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{3} {\mathrm e}^{x^{3}}}{6}-\frac {{\mathrm e}^{x^{3}}}{12}+{\mathrm e}^{-x^{3}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.104 (sec). Leaf size: 32

DSolve[D[y[x],x]+3*x^2*y[x]==x^5*Exp[x^3],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^{x^3} \left (2 x^3-1\right )+c_1 e^{-x^3} \]