(b) y''+y′+3⋅a5y=0

Question
Differential equations
asked 2021-03-11
\(\displaystyle{\left({b}\right)}{y}{''}+{y}′+{3}⋅{a}{5}{y}={0}\)

Answers (1)

2021-03-12
The characteristic equation of this Differential equations is \(\displaystyle{r}^{{2}}+{r}+{3.25}={0}\)
Solve this quadratic equation: \(\displaystyle{r}=\frac{{-{1}\pm\sqrt{{{1}-{13}}}}}{{2}}=\frac{{-{1}\pm\sqrt{{12}}}}{{2}}=\frac{{-{1}\pm{2}{i}\sqrt{{3}}}}{{2}}=-{\left(\frac{{1}}{{2}}\right)}\pm{i}\sqrt{{3}}\)
Therefore, the solution is \(\displaystyle{y}={C}{1}{\left(\frac{{e}^{{-{{x}}}}}{{2}}\right)}{\cos{{\left({x}\sqrt{{3}}\right)}}}+{C}{2}{\left(\frac{{e}^{{-{{x}}}}}{{2}}\right)}{\sin{{\left({x}\sqrt{{3}}\right)}}}\)
0

Relevant Questions

asked 2020-12-06
Find solution of \(\displaystyle{y}′{\left({t}\right)}={k}{y}{\left({t}\right)}\) with y(1) = 5 y′(1) = 4. \(\displaystyle{y}={C}{e}^{{{k}{t}}}\)
asked 2020-11-24
Q. 1# \((a−x)dy+(a+y)dx=0(a−x)dy+(a+y)dx=0\)
asked 2021-01-31
Q. 1# \(\displaystyle{\left({a}−{x}\right)}{\left.{d}{y}\right.}+{\left({a}+{y}\right)}{\left.{d}{x}\right.}={0}{\left({a}−{x}\right)}{\left.{d}{y}\right.}+{\left({a}+{y}\right)}{\left.{d}{x}\right.}={0}\)
asked 2020-11-12
If \(\displaystyle{x}{y}+{6}{e}^{{{y}}}={6}{e}\), find the value of y" at the point where x = 0.
asked 2021-01-08
Solve the Differential equations \(\displaystyle{\left({D}^{{3}}−{3}{D}+{2}\right)}{y}={0}\)
asked 2020-11-09
solve the Differential equations \(\displaystyle{y}{'''}+{10}{y}{''}+{25}{y}'={0}\)
asked 2021-01-02
Solve this equation pls \(\displaystyle{y}'+{x}{y}={e}^{{x}}\)
\(\displaystyle{y}{\left({0}\right)}={1}\)
asked 2021-03-05
Solve differential equation: \(\displaystyle{y}'+{y}^{{2}}{\sin{{x}}}={0}\)
asked 2021-02-21
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.
\(\displaystyle{\left[\lambda_{{{1}}}=-{1}\Rightarrow\le{f}{t}{\left\lbrace{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}{0}{3}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace},\lambda_{{{2}}}={3}{i}\Rightarrow\le{f}{t}{\left\lbrace{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}-{i}{1}+{i}{7}{i}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace},\lambda_{{3}}=-{3}{i}\Rightarrow\le{f}{t}{\left\lbrace{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}+{i}{1}-{i}-{7}{i}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace}\right]}\)
asked 2021-01-04
Solve the initial value problem.
\(\displaystyle{4}{x}^{{2}}{y}{''}+{17}{y}={0},{y}{\left({1}\right)}=-{1},{y}'{\left({1}\right)}=-\frac{{1}}{{2}}\)
...