The solution of the first order differential equation \(x^{ \prime }(t)=-3x(t),x(0)={ x }_{ 0 }\) is
A\(x(t)={ x }_{ 0 }e^{ -3t }\)
B\(x(t)={ x }_{ 0 }e^{ -3 }\)
C\({ x }_{ 0 }e^{ -1/3 }\)
D\({ x }_{ 0 }e^{ -t }\)
Question - 2
For the equation x"(t)+3x'+2x(t) = 5, the solution x(t) approaches which of the following values as \(t\rightarrow \infty \)?
A0
B5/2
C5
D10
Question - 3
The order and degree of the differential equation \(\frac { { d }^{ 3 }y }{ dx^{ 2 } } +4\sqrt { \left( \frac { dy }{ dx } \right) ^{ 3 }+{ y }^{ 2 }=0 } \) are respectively
A3 and 2
B2 and 3
C3 and 3
D3 and 1
Question - 4
The general solution of \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +y=0\) is
Ay = P cos x + Q sin x
By = P cos x
Cy = P sin x
Dy = P \(sin^{ 2 }x\)
Question - 5
The degree of the differential equation \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +2{ x }^{ 3 }=0\) is
A0
B1
C2
D3
Question - 6
The solution for the differential equation \(\frac { dy }{ dx } ={ x }^{ 2 }y\) with the condition that y = 1 at x = 0 is
A\(y={ e }^{ 1/2x }\)
B\(logy=\frac { { x }^{ 3 } }{ 3 } +4\)
C\(logy=\frac { { x }^{ 2 } }{ 2 } \)
D\(y=e^{ x^{ 3 }/3 }\)
Question - 7
The solution of the differential equation \(\frac { dy }{ dx } +\frac { y }{ x } =x\) with the condition that y = 1 at x = 1 is