1-) Consider the following differential equation,
y''(x)-e^(y'(x))^2+3y(x)=x.
Which of following statements below is correct?
a) Fourth order, linear.
b) Fourth order, nonlinear.
c) Third order, linear.
d) Third order, nonlinear.
e) Second order, nonlinear.
2-) What is the solution of following initial value problem?
\frac{dy}{dx} = \frac{x^2}{y}, \quad y(0) = 1.
a) y(x) = \sqrt{x^2+1}
b) y(x) = \sqrt{x^2-1}
c) y(x) = \sqrt{x^2+1}
d) y(x) = \sqrt{x^2-1}
e) y(x) = \sqrt{x^2+1}
