5. Find explicit particular solution of the initial value problem a) dy – 3x(y² +1), y(0) =1 %3D dx dy b) 2y dx Vx? -16 y(5)= 2 %3D c) ay = 2.xy + 3x?y', y(1)=-1 dy %3D dx d) dy 6e2-, y(0)=0 dr
5. Find explicit particular solution of the initial value problem a) dy – 3x(y² +1), y(0) =1 %3D dx dy b) 2y dx Vx? -16 y(5)= 2 %3D c) ay = 2.xy + 3x?y', y(1)=-1 dy %3D dx d) dy 6e2-, y(0)=0 dr
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Solve the Initial Value Problems
Given below are differential equations with their respective initial conditions. The task is to find an explicit particular solution for each initial value problem.
#### a) Differential Equation:
\[ \frac{dy}{dx} = 3x^2(y^2 + 1), \]
with the initial condition,
\[ y(0) = 1 \]
#### b) Differential Equation:
\[ 2y \frac{dy}{dx} = \frac{x}{\sqrt{x^2 - 16}}, \]
with the initial condition,
\[ y(5) = 2 \]
#### c) Differential Equation:
\[ \frac{dy}{dx} = 2xy^2 + 3x^2 y^2, \]
with the initial condition,
\[ y(1) = -1 \]
#### d) Differential Equation:
\[ \frac{dy}{dx} = 6e^{2x-y}, \]
with the initial condition,
\[ y(0) = 0 \]
#### e) Differential Equation:
\[ \frac{dy}{dx} = x^3(1 - y), \]
with the initial condition,
\[ y(0) = 3 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3861071f-90cb-4097-84b9-a523b25fee85%2Ff7ef7d06-b61d-4478-a2b1-d48ad28cdb56%2Fempzinl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solve the Initial Value Problems
Given below are differential equations with their respective initial conditions. The task is to find an explicit particular solution for each initial value problem.
#### a) Differential Equation:
\[ \frac{dy}{dx} = 3x^2(y^2 + 1), \]
with the initial condition,
\[ y(0) = 1 \]
#### b) Differential Equation:
\[ 2y \frac{dy}{dx} = \frac{x}{\sqrt{x^2 - 16}}, \]
with the initial condition,
\[ y(5) = 2 \]
#### c) Differential Equation:
\[ \frac{dy}{dx} = 2xy^2 + 3x^2 y^2, \]
with the initial condition,
\[ y(1) = -1 \]
#### d) Differential Equation:
\[ \frac{dy}{dx} = 6e^{2x-y}, \]
with the initial condition,
\[ y(0) = 0 \]
#### e) Differential Equation:
\[ \frac{dy}{dx} = x^3(1 - y), \]
with the initial condition,
\[ y(0) = 3 \]
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