Solve the differential equation (1+x2) racdydx = 2xy, given that y=1 when x=0.

Here are the solutions to the questions: (ii) Solve the differential equation (1+x²)(dy)/(dx) = 2xy, given that y=1 when x=0. Step 1: Separate the variables. (1+x²)(dy)/(dx) = 2xy; dy/y = (2x)/(1+x²) dx Step 2: Integrate both sides. ∫ 1/y dy = ∫ (2x)/(1+x²) dx; ln|y| = ln(1+x²) + C Note

Solve the differential equation (1+x2) racdydx = 2xy, given that y=1 when x=0.

Here are the solutions to the questions: (ii) Solve the differential equation (1+x²)(dy)/(dx) = 2xy, given that y=1 when x=0. Step 1: Separate the variables. (1+x²)(dy)/(dx) = 2xy; dy/y = (2x)/(1+x²) dx Step 2: Integrate both sides. ∫ 1/y dy = ∫ (2x)/(1+x²) dx; ln|y| = ln(1+x²) + C Note

Solved: Solve the differential equation (1+x2) racdydx…

Here are the solutions to the questions:

(ii) Solve the differential equation $(1+x^2)\frac{dy}{dx} = 2xy$ , given that $y=1$ when $x=0$ .

Separate the variables.
$(1+x^2)\frac{dy}{dx} = 2xy$ $\frac{dy}{y} = \frac{2x}{1+x^2}\,dx$
Integrate both sides.
$\int \frac{1}{y}\,dy = \int \frac{2x}{1+x^2}\,dx$ $\ln|y| = \ln(1+x^2) + C$
Note

Solve the differential equation (1+x2) racdydx = 2xy, given that y=1 when x=0.

Step-by-step solution

Separate the variables.

Integrate both sides.

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