Download GUJRANWALA GURU NANAK PUBLIC SCHOOL MATHS

GUJRANWALA GURU NANAK PUBLIC SCHOOL
MATHS ASIGNMENMENT -XII
TOPIC : DIFFERENTIAL EQUATIONS
1. Show that y = 4 sin 3 x is the solution of the differential equation
d2y/dx2 + 9y = 0 .
2. Solve the differential equation :
dy/dx +
1+ y2 / y = 0.
3. Find the general solution of equation : dy/ dx = 1- cos4x / 1+ cos4x .
4. Find the solution : ( y 5 tan
-1
5. Solve the problem e dy / dx
= x + 1 , y( 0) = 5 .
6. Solve
dy/dx = e
x+y
y3 ) dy = dx .
+ x2 e y .
7. Solve √1 + x2 + y 2 + x2 y2 + xy dy/dx .
8. Solve y – x dy/dx = 2 ( 1 + x2 dy / dx ) , y ( 1 ) = 1 .
9. Solve dy / dx = ( 4x + y + 1) 2 .
10. Solve dy/ dx = sin(x+ y) + cos (x+ y) .
11. Solve the differential equation : dy/ dx = x( 2y – x) / x( 2y + x) , y(1) = 1 ( by telling
About homogenous).
12. Solve the linear diff eqn : dy/dx + ay = e mx .
13. Solve ( x2 – 1 ) dy/dx + 2 ( x + 2 ) y = 2 ( x+ 1 )
14. Solve x dy = ( y + 2 x 2 ) dx
15. Solve x log x dy / dx + y = 2 logx .
16. Solve the initial value problem : x dy/dx + y = xcosx + sinx , y( π / 2 ) = 1 .
17. Solve ( 1 + y + x 2 y ) dx + ( x + x 3 ) dy = 0 , y ( 1) = 1 .
18. Solve
dy/dx + y cotx = x2 cotx + 2x
END