Teaching HSSC TGT 2023 Mock Test (Latest Pattern) Engineering Mathematics Differential Equations Higher Order Linear Differential Equations with Constant Coefficients
The general solution of the differential equation \(\frac{{{d^2}y}}{{d{x^2}}} + \frac{{dy}}{{dx}} - 6y = x\) is given by:
1
\(y = {c_1}{e^{3x}} + {c_2}{e^{ - 2x}} - \frac{{6x + 1}}{{36}}\)
2
\(y = {c_1}{e^{ - 3x}} + {c_2}{e^{2x}} - \frac{x}{6} - \frac{1}{{36}}\)
3
\(y = {c_1}{e^{ - 3x}} + {c_2}{e^{2x}} + \frac{x}{6} + \frac{1}{{36}}\)
4
\(y = {c_1}{e^{3x}} + {e^{2x}} + \frac{x}{6} + \frac{1}{{36}}\)
5
Not Attempted