Class 12 ISC Maths Chapter Diffrential Equations Exercise 9.6
Access a comprehensive collection of Differential Equations questions, specially designed to help you grasp and apply this important mathematical topic. Our question bank covers various types of differential equations, including first-order, second-order, homogeneous, and non-homogeneous equations, along with real-world applications in physics, engineering, and other fields. These practice questions will help you reinforce your problem-solving skills, deepen your conceptual understanding, and prepare effectively for exams. Whether you're a student or a learner aiming to master Differential Equations, our collection offers the perfect resource for practice and success.
class 12 differential-equations exercise9-6
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Q2 Which of the following differential equations are homogeneous? - (x - y) dy / dx =x+2y
- y-x dy / dx =x+y dy / dx
- (x2 + 3xy - 4y2) dx - x (x2 + 2y) dy = 0
- x dy / dx +y=xtan-1 y / x
- x cos( y / x ) dy / dx =y cos ( y / x ) -3x2
- x dy / dx -y=√x2 +y2
- (x2 +y2sin x / y ) dy / dx =2xy ex/y
- 2y e1/y dx + (y-2x e1/y ) dy=0
- ydx +xlog ( y / x )dy-2x dy=0
dy / dx
=x+2y dy / dx
=x+y dy / dx
dy / dx
+y=xtan-1 y / x
y / x
) dy / dx
=y cos ( y / x
) -3x2 dy / dx
-y=√x2 +y2 x / y
) dy / dx
=2xy ex/y y / x
)dy-2x dy=0
Q11 Solve the differential equation (x + y) dy + (x - y) dx = 0, given that y =1 when x = 1
Q12 Solve the differential equation (x2 - y2) dx + 2xy dy = 0, given that y = 1 when x = 1
Q13 Find particular solutions of the following differential equations : - 2xy +y2 -2x2 dy / dx = 0, given that y (1) = 2
- dy / dx - y / x +cosec ( y / x ) =0,given that y=0 when x=1
- x ey/x-y +x dy / dx =0,given that y(e)=0
dy / dx
= 0, given that y (1) = 2 dy / dx
- y / x
+cosec ( y / x
) =0,given that y=0 when x=1 dy / dx
=0,given that y(e)=0
Q14 Show that the following differential equations are homogeneous and find their particular solutions : - x dy / dx sin( y / x ) +x -y sin y / x =0,given that x=1 when y= π/2
- (x ey/x+ y)dx=x dy,given that y=0 when x=1
dy / dx
sin( y / x
) +x -y sin y / x
=0,given that x=1 when y= π/2 
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