Particular Solution as a Definite Integral

Question

Let $$y=p(x)$$ be the particular solution to the differential equation $$\frac{dy}{dx}=\ln(1+x^2)$$ satisfying the initial condition $$p(-1)=0$$. Which of the following is an expression for $$p(x)$$?

Accepted Answer

$$p(x)=\int_{-1}^x\ln(1+t^2)\, dt$$

Answer

$$p(x)=\frac{2x}{1+x^2}$$

Answer

$$p(x)=x\ln(1+x^2)-2x+2\arctan(x)$$

Answer

$$p(x)=\int_0^x\ln(1+t^2)\, dt$$

Particular Solution as a Definite Integral

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