DIFFERENTIAL EQUATION CLASS 12

dy/dx = 2x/e^2y find the general solution

• y = ln (2x/2 + C)

  2

• y = ln(2x/2)+c

• y = e^2x+c

• y = mx+b

Dy/dx= tanx+15x2+e^x+1/x

• y= -ln|sinx| + 5x³ + e^x + ln|x| + c

• y= secxtanx + 5x³ + e^x + ln|x| + c

• y= -ln|cosx| + 5x³ + e^x + ln|x| + c

• y= sec²(x) + 5x³ + e^x + ln|x| + c

Find the particular solution for y if dy/dx = 2x√y and y = 4 when x = 3.

• 2√y = x² + C

• y = (x² + 25)²/4

• y = (x²/2-5/2)^1/2

• y = x⁴/4

dy/dx = 4x/y.  Suppose y(0)=1
The particular solution is

• B
• C
• D
• E

Tags

CCSS.HSA.REI.A.1

Determine the order and degree.

• 1, 2
• 2, 2
• 1, 1
• 2, 1

What is the order and degree of the differential equation?

• 1, 2
• 2, 1
• 3, 2
• 2, 3

What is the order of the D.E. (d²y/dx²)²+ y = 0

• 1

• 2

• 3

• 0

Integrating factor of the differential equation  $x\frac{\text{d}y}{\text{d}x}-y=\sin x$  

•  $-\frac{1}{x}$  

•  $\frac{1}{x}$  

•  $\ln\left|x\right|$  

•  $\frac{1}{x^2}$  

The solution of linear differential equation  $x\frac{\text{d}y}{\text{d}x}+2y=x^2$  

•  $y=\frac{x^2+c}{4x^2}$  

•  $y=\frac{x^2}{4}+c$  

•  $y=\frac{x^4+c}{x^2}$  

•  $y=\frac{x^4+c}{4x^2}$  

By separation of variables, solve the resulting equations $\int\ \frac{v}{v+1}dv=\int_{ }^{ }\ \frac{1}{y}dy\text{}$  

•  $\frac{x}{y}-\ln\left|\frac{x}{y}+1\right|=\ln y+C$  

•  $\frac{x}{y}+\ln\left|\frac{x}{y}+1\right|=\ln y+C$  

•  $\frac{x}{y}+\frac{x^2}{2y^2}=\ln y+C$  

•  $\frac{x}{y}-\frac{x^2}{2y^2}=\ln y+C$