Question

Determine order and degree (if defined) of differential equations given in the following.

1. $\frac{d^{4}y}{d{x}^4}+\sin \left(y^{\prime \prime \prime }\right)=0$
2. $y^{\prime }+5y=0$
3. ${\left(\frac{ds}{dt}\right)}^4+3s\frac{d^{2}s}{d{t}^2}=0$

4. ${\left(\frac{d^{2}y}{d{x}^2}\right)}^2-\cos \left(\frac{dy}{dx}\right)=0$
5. $\frac{d^{2}y}{d{x}^2}=\cos 3x+\sin 3x$
6. $(y^{\prime \prime \prime }{)}^2+(y{)}^3+(y{)}^4+y^5=0$
7. $y+2y^{\prime \prime }+y=0$
8. $y^{\prime }+y=e^x$
9. $y^{\prime \prime }+\left(y\right)2+2y=0$
10. $y^{\prime \prime }+2y+\sin y=0$

Answer 1

1. $\frac{d^{4}y}{d{x}^4}+\sin \left(y^{\prime \prime \prime }\right)=0$

Order $=4$

Degree $=1$

2. $y^{\prime }+5y=0$

Order $=1$

Degree $=1$

3. ${\left(\frac{ds}{dt}\right)}^4+3s\frac{d^{2}s}{d{t}^2}=0$

Order $=2$

Degree $=1$

4. ${\left(\frac{d^{2}y}{d{x}^2}\right)}^2-\cos \left(\frac{dy}{dx}\right)=0$

Order $=2$

Degree $=2$

5. $\frac{d^{2}y}{d{x}^2}=\cos 3x+\sin 3x$

Order $=2$

Degree $=1$

6. $(y^{\prime \prime \prime }{)}^2+(y{)}^3+(y{)}^4+y^5=0$

Order $=3$

Degree $=2$

7. $y+2y^{\prime \prime }+y=0$

Order $=2$

Degree $=1$

8. $y^{\prime }+y=e^x$

Order $=1$

Degree $=1$

9. $y^{\prime \prime }+\left(y\right)2+2y=0$

Order $=2$

Degree $=1$

10. $y^{\prime \prime }+2y+\sin y=0$

Order $=2$

Degree $=1$