These are equations, Calculus-style. From modeling real-world phenomenon, from the path of a rocket to the cooling of a physical object, Differential Equations are all around us.

Which of the following differential equations is a linear equation of order \(3:\)
\[\begin{align}
&(a) \frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}\frac{dy}{dx}+y=5x\\
&(b) \frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}+y^2=x^2+3x\\
&(c) x\frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}=e^x\\
&(d) \frac{d^2y}{dx^2}+\frac{dy}{dx}=\log{x}?
\end{align}\]

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

If \(a\) and \(b\) are the order and the degree, respectively, of the differential equation
\[\left(\frac{d^{4}y}{dx^{4}}\right)^{8}-\left(\frac{dy}{dx}\right)^{25}+15=0,\]
what is the value of \(b-a?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

Which of the following differential equations has degree \(1 ?\)
\[\begin{align}
&\text{(a) } x^3\frac{d^2y}{dx^2}+(x+x^2)\left(\frac{dy}{dx}\right)^2+e^xy^3=2\sin x \\
&\text{(b) } y=2\frac{dy}{dx}+5\sqrt{1-\left(\frac{dy}{dx}\right)^2} \\
&\text{(c) } \sqrt{\frac{dy}{dx}+y}=x+4
\end{align}\]

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!