Examples of Particular Solutions

Examples of Particular Solutions
EDU» dsolve('D2y + 3*Dy + 2*y = 1 + x + 3*x^2
- 4*x^3','x')
ans =
1/2*(55*exp(x)-50*x*exp(x)+21*x^2*exp(x)4*x^3*exp(x)+2*C1*exp(-2*x)*exp(x)+2*C2)/exp(x)
EDU» simplify(ans)
ans =
55/2-25*x+21/2*x^2-2*x^3
+C1*exp(-2*x)+C2*exp(-x)
EDU» dsolve('D2y + 3*Dy + 2*y = (1 + x + 3*x^2
- 4*x^3)*exp(x)','x')
ans =
-1/54*(150*exp(x)^2*x-95*exp(x)^2117*exp(x)^2*x^2+36*exp(x)^2*x^3-54*C1*exp(2*x)*exp(x)-54*C2)/exp(x)
EDU» simplify(ans)
ans =
-1/54*(150*x-95-117*x^2+36*x^3
-54*C1*exp(-3*x)-54*C2*exp(-2*x))*exp(x)
EDU» dsolve('D2y + 3*Dy + 2*y = (1 + x + 3*x^2
- 4*x^3)*sin(x)','x')
ans =
-1/1250*(-7035*cos(x)*x*exp(x)+13*exp(x)*cos(x)9005*exp(x)*sin(x)*x+8884*exp(x)*sin(x)+6225*cos(x)*
x^2*exp(x)+1425*exp(x)*sin(x)*x^21500*cos(x)*x^3*exp(x)+500*sin(x)*x^3*exp(x)1250*C1*exp(-2*x)*exp(x)-1250*C2)/exp(x)
EDU» simplify(ans)
ans =
1407/250*cos(x)*x-13/1250*cos(x)+1801/250*sin(x)*x4442/625*sin(x)-249/50*cos(x)*x^257/50*sin(x)*x^2+6/5*cos(x)*x^3-2/5*sin(x)*x^3
+C1*exp(-2*x)+C2*exp(-x)
EDU» dsolve('D2y + 3*Dy + 2*y = (1 + x + 3*x^2
- 4*x^3)*exp(-2*x)','x')
ans =
1/2*(32*exp(-2*x)*x*exp(x)+17*exp(2*x)*x^2*exp(x)+6*exp(-2*x)*x^3*exp(x)+2*exp(2*x)*x^4*exp(x)+32*exp(-2*x)*exp(x)+2*C1*exp(2*x)*exp(x)+2*C2)/exp(x)
EDU» simplify(ans)
ans =
1/2*(32*x*exp(-x)+17*x^2*exp(-x)+6*x^3*exp(x)+2*x^4*exp(-x)+32*exp(-x)
+2*C1*exp(-x)+2*C2)*exp(-x)
EDU» dsolve('D2y + y = cos(t)','t')
ans =
1/2*sin(t)*t
+C1*sin(t)+C2*cos(t)
EDU» dsolve('D2y + y = t*cos(t)','t')
ans =
1/4*sin(t)*t^2+1/4*t*cos(t)-1/4*sin(t)
+C1*sin(t)+C2*cos(t)