Mister Exam

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x.diff(x)=5x-3y equation

The teacher will be very surprised to see your correct solution 😉

You have entered [src]

/x  for 0 = 1            
|                        
<1  for 1 = 1 = 5*x - 3*y
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\0  otherwise

$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 5 x - 3 y$$

Simplify

The graph

Sum and product of roots [src]

sum

  1   5*re(x)   5*I*im(x)
- - + ------- + ---------
  3      3          3

$$\frac{5 \operatorname{re}{\left(x\right)}}{3} + \frac{5 i \operatorname{im}{\left(x\right)}}{3} - \frac{1}{3}$$

  1   5*re(x)   5*I*im(x)
- - + ------- + ---------
  3      3          3

$$\frac{5 \operatorname{re}{\left(x\right)}}{3} + \frac{5 i \operatorname{im}{\left(x\right)}}{3} - \frac{1}{3}$$

product

  1   5*re(x)   5*I*im(x)
- - + ------- + ---------
  3      3          3

$$\frac{5 \operatorname{re}{\left(x\right)}}{3} + \frac{5 i \operatorname{im}{\left(x\right)}}{3} - \frac{1}{3}$$

  1   5*re(x)   5*I*im(x)
- - + ------- + ---------
  3      3          3

$$\frac{5 \operatorname{re}{\left(x\right)}}{3} + \frac{5 i \operatorname{im}{\left(x\right)}}{3} - \frac{1}{3}$$

-1/3 + 5*re(x)/3 + 5*i*im(x)/3

Rapid solution [src]

       1   5*re(x)   5*I*im(x)
y1 = - - + ------- + ---------
       3      3          3

$$y_{1} = \frac{5 \operatorname{re}{\left(x\right)}}{3} + \frac{5 i \operatorname{im}{\left(x\right)}}{3} - \frac{1}{3}$$

y1 = 5*re(x)/3 + 5*i*im(x)/3 - 1/3

x.diff(x)=5*x-3*y equation