state gov RPSC 2nd Grade Senior Teacher Mock Test Series 2025 Engineering Mathematics Differential Equations Higher Order Linear Differential Equations with Constant Coefficients
The solution of the differential equation \(\frac{{{d^3}y}}{{d{x^3}}} - 9\frac{{dy}}{{dx}} = \cos x\) is
1
\(y\left( x \right) = {C_1}{e^{3x}} + {C_2}{e^{ - 3x}} + {C_3} - \frac{1}{{10}}\sin x\)
2
\(y\left( x \right) = {C_1}{e^{3x}} + {C_2}{e^{ - 3x}} + {C_3} + \frac{1}{{10}}\cos x\)
3
\(y\left( x \right) = {C_1}{e^{3x}} + {C_2}{e^{ - 3x}} + {C_3} + \frac{1}{{10}}\sin x\)
4
\(y\left( x \right) = {C_1}{e^{3x}} + {C_2}{e^{ - 3x}} + {C_3} - \frac{1}{{10}}\cos x\)
5
Question Not Attempted