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Differential Equations
Examples
4
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Order and Degree
Order
Order is the highest differential appearing a differential equation
Degree
Degree is highest power of highest differential after converting D.E.
to polynomial form (remove fractional powers if any)
e.g.
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Find order and degree of the following differential equation
(1)
(2)
(3)
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Formation of Differential Equation
Differentiate
Family of Curves Differential
Equation
Integrate
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The differential equation for the family of circle x2 + y2 - 2ay = 0, where is an
arbitrary constant is
A. (x2 + y2)y’ = 2xy B. 2(x2 + y2)y’ = xy
C. (x2 - y2)y’ = 2xy D. 2(x2 - y2)y’ = xy
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A.
B. JEE M 2021
C.
D.
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Solution of Differential Equation
Differentiate
Family of Curves Differential
Equation
Integrate
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Differential Equation
Variable
Separable
Homogeneous Linear
Reducible
Reducible to Reducible to Linear
Variable
Homogeneous (Bernoulli's D.E.)
Separable
T-1 T-2 T-3
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Variable Separable
Solve the following differential equation
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A.
B.
JEE M 2021
C.
D.
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Let y = y1(x) and y = y2(x) be the solution curves the differential equation
dy/dx = y + 7 with initial conditions y1(0) = 0 and y2(0) = 1 respectively. Then the curves y =
y1(x) and y = y2(x) intersect at
(A) No point
(B) Two points JEE M 2023
(C) One point
(D) Infinite number of points
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Reducible Variable Separable: Type 1
Standard Form:
Method: Put ax + by + c = t
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Solve
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Solve
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Reducible Variable Separable: Type 2
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Solve the differential equation
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Reducible Variable Separable: Type 3
1 i. x dx + y dy = r dr ii. x dy - y dx = r2 dθ
2 i. x dx - y dy = r dr ii. x dy - y dx = r2 sec θ dθ
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Solve the following differential Equation
xdx + ydy = x (xdy - ydx)
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Solve the following differential Equation
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Method to solve Homogeneous Differential Equation
Solve
A. x2y = c(2x + y) B. x2y = c(2x - y)
C. yx = c(2x + y) D. xy = c(2x - y)
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Linear Differential Equation
#Standard form of L.D.E of first order
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Reducible Linear Differential Equation
#Standard form of Reducible L.D.E
#Method to solve Reducible L.D.E
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Solve the following differential equations
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JEE M 2023
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Exact Differential Equation
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Solve
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Solutions of the differential equation ydx + (x + x2y)dy = 0 is
A. log y = C B.
C. D.
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Thank You #VCians
