# Here's what students ask on Differential equations

Differential equations

### How to integrate $$\displaystyle{{\cos}^{{2}}{\left({2}{x}\right)}}$$?

Differential equations

### $$\displaystyle{\left({b}\right)}{y}{''}+{y}′+{3}⋅{a}{5}{y}={0}$$

Differential equations

### Solve differential equation: $$\displaystyle{y}'+{y}^{{2}}{\sin{{x}}}={0}$$

Differential equations

### Make and solve the given equation $$x\ dx\ +\ y\ dy=a^{2}\frac{x\ dy\ -\ y\ dx}{x^{2}\ +\ y^{2}}$$

Differential equations

### Give the correct answer and solve the given equation: $$\displaystyle{y}\ \text{ - 4y}+{3}{y}={x},{y}_{{1}}={e}^{x}$$

Differential equations

### The coefficient matrix for a system of linear differential equations of the form $$\displaystyle{y}^{{{1}}}={A}_{{{y}}}$$ has the given eigenvalues and eigenspace bases. Find the general solution for the system. $$\displaystyle{\left[\lambda_{{{1}}}=-{1}\Rightarrow\le{f}{t}{\left\lbrace{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}{0}{3}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace},\lambda_{{{2}}}={3}{i}\Rightarrow\le{f}{t}{\left\lbrace{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}-{i}{1}+{i}{7}{i}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace},\lambda_{{3}}=-{3}{i}\Rightarrow\le{f}{t}{\left\lbrace{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}+{i}{1}-{i}-{7}{i}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace}\right]}$$

Differential equations

### Determine whether three series converges or diverges. if it converges, find its sum $$\displaystyle{\sum_{{{n}={0}}}^{{\infty}}}\frac{{{\left(-{1}\right)}^{{n}}}}{{4}^{{n}}}$$

Differential equations

### Solve the given system of differential equations. \[Dx+Dy+(D+1)z=0\) Dx+y=e^{t}\) Dx+y-2z=50\sin(2t)\)

Differential equations

### Solve the Differential equations $$y'' + 4y = 4 \tan^{2} x$$

Differential equations

### Find the general solution to the equation $$\displaystyle{x}{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}+{3}{\left({y}+{x}^{2}\right)}=\frac{{ \sin{{x}}}}{{x}}$$

Differential equations

### Find the differential of the function. $$\displaystyle{T}=\frac{{v}}{{1}}+{u}{v}{w}$$

Differential equations

### Solve $$\left(d^{2}\frac{y}{dt^{2}}\right)\ +\ 7\left(\frac{dy}{dt}\right)\ +\ 10y=4te^{-3}t$$ with $$y(0)=0,\ y'(0)=\ -1$$

Differential equations

### Determine the following integral $$\displaystyle\int{\left({{\sin}^{{2}}{\left({2}{x}\right)}}+{{\cos}^{{2}}{\left({2}{x}\right)}}\right)}{\left({x}^{{2}}-{2}{\cos{\pi}}+\frac{{2}}{{x}^{{2}}}\right)}{)}{\left.{d}{x}\right.}$$

Differential equations

### Find the solution $$\displaystyle{\left({x}\frac{{\sin{{y}}}}{{x}}\right)}{\left.{d}{y}\right.}={\left({y}\frac{{\sin{{y}}}}{{x}}-{x}\right)}{\left.{d}{x}\right.}$$

Differential equations

### Find $$\displaystyle\frac{{\left.{d}{x}\right.}}{{\left.{d}{y}\right.}}$$ if $$\displaystyle{y}={\sin{{2}}}{x}$$

Differential equations

### Solve the Bernoulli Differential equations. $$\displaystyle{x}{y}′-{y}={x}{y}^{{5}}$$

Differential equations

### Solve $$\displaystyle\sqrt{{{16}-{x}^{{2}}}}$$ between -4 and 0

Differential equations

### $$x^{2} +y^{2} =25$$ What is dydx dx/dy?

Differential equations