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Published on: 27/08/2019
Differential Equations
Download Tamil Nadu 12th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
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1.
The degree of c =\(\frac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 3 } \right] ^{ 2/3 } }{ \frac { d^{ 3 }y }{ dx^{ 3 } } } \) where c is a constant is _____________
1
3
-2
2
2.
The degree of the differential equation \(\sqrt { 1+\left( \frac { { d }y }{ dx } \right) ^{ \frac { 1 }{ 3 } } } =\frac { { d }^{ 2 }y }{ dx^{ 2 } } \) is _____________
1
2
3
6
3.
The differential equation formed by eliminating A and B from y = ex (A cos x + B sin x) is _____________
y2+y1= 0
y2-y1 = 0
y2-2y1+2y = 0
y2-2y1-2y = 0
4.
The differential equation obtained by eliminating a and b from y = a e3x + b e-3x is _____________
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)+ay = 0
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)-9y = 0
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -9\frac { dy }{ dx } \)
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)+9x = 0
5.
If y = k.eλx then its differential equation where k is arbitrary constant is _____________
\(\frac { dy }{ dx } \)= λy
\(\frac { dy }{ dx } \)= ky
\(\frac { dy }{ dx } \)+ky = 0
\(\frac { dy }{ dx } \)= eλx
6.
The differential equation satisfied by all the straight lines in xy plane is _____________
\(\frac { dy }{ dx } \)=a constant
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)=0
y+ \(\frac { dy }{ dx } \) = 0
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)+y=0
7.
The differential equation of y = mx + c is ______.(m and c are arbitrary constants)
\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \) = 0
y = x \(\frac { dy }{ dx } \) + c
xdy + ydx = 0
ydx − xdy = 0
8.
The complementary function of (D2+ 4)y = e2x is ______.
(Ax +B)e2x
(Ax +B)e−2x
A cos 2x + B sin 2x
Ae−2x+ Be2x
9.
The differential equation formed by eliminating a and b from \(y=a e^{x}+b e^{-x}\) is ______.
\(\frac{d^{2} y}{d x^{2}}-y=0\)
\(\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0\)
\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0\)
\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -x=0\)
10.
The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.
1
2
3
4
11.
I.F. of \(\frac { dy }{ dx } \)+Py = Q
12.
I.F. of \(\frac { dy }{ dx } \)+Px = Q
13.
General form of linear equation
14.
Degree of linear differential equation
15.
y = mx
1.
(a)
1
2.
(d)
6
3.
(c)
y2-2y1+2y = 0
4.
(b)
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)-9y = 0
5.
(a)
\(\frac { dy }{ dx } \)= λy
6.
(b)
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)=0
7.
(a)
\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \) = 0
8.
(c)
A cos 2x + B sin 2x
9.
(a)
\(\frac{d^{2} y}{d x^{2}}-y=0\)
10.
(a)
1
11.
\(e^{ \int { pdx } }\)
12.
\(e^{ \int { pdy } }\)
13.
\(\frac { dy }{ dx } \)+Py = Q
14.
1
15.
Family of lines
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